Question

How many solutions will this system of equations have?
y = 3.5x - 3.5

y = -3.5x + 3.5


No solution
Infinite solutions
One solution
Two solutions

Answer 1

Well, we know that if two lines are parallel and have the same intercept, they are actually the same line, and have an infinite number of solutions.

If two lines are parallel, but different intercepts, they will never meet, so there are no solutions. Parallel lines will have slopes that are equal (they'll both have the same slope).

If two lines have different slopes, they'll meet at exact one point. Meaning, there will be a single solution to the system of equations.

Which category do these lines fall in?

Answer 2

Infinite solutions

Answer 3

Not infinite. What are the slopes of the two lines?

Answer 4

I'm not sure what part of the equation is the slope

Answer 5

y=mx+b

m is the slope (it's the number that's multiplying the x), b is the "y-intercept."

Answer 6

So -3.5x and 3.5x

Answer 7

Right, so the slopes are 3.5 and -3.5

These aren't the same, so how many solutions are there?

Answer 8

Two

Answer 9

No. Read my first post again.

Answer 10

O One solution

Answer 11

There you go. One solution :)

Answer 12

Thank you :)